HETEROCLINIC ORBITS, MOBILITY PARAMETERS AND STABILITY FOR THIN FILM TYPE EQUATIONS
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Bibliographic record
Abstract
. We study numerically the phase space of the evolution equation h t = (h n h xxx ) x B(h m h x ) x : Here h(x; t) 0, n > 0 and m 2 R, and the Bond number B is positive. We pursue three goals: to investigate the nonlinear stability of the positive periodic and constant steady states; to locate heteroclinic connecting orbits between these steady states and the compactly supported `droplet' steady states; and to determine how these orbits change when the `mobility' exponents n and m are changed. For example, when n + 1 m < n + 2 we know from the companion article that there can be three fundamentally dierent steady states with the same period and volume. The rst is a constant steady state that is a local minimum of the energy. The second is a positive periodic steady state that is a saddle for the energy and has higher energy than the constant steady state. The third is a periodic collection of droplet steady states having lower energy than either the positive or co...
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it